Suppose that there are two identically-looking batteries in a box. The first one should last for a time that is exponentially distributed with parameter λ1 = 1 (in months). The second one should last for a time that is exponentially distributed with parameter λ2 = 2. A battery has been picked randomly and is still working after two months. Given this information, what is the probability that the first battery was picked?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Suppose that there are two identically-looking batteries in a box. The first one should last for a time that is exponentially distributed with parameter λ1 = 1 (in months). The second one should last for a time that is exponentially distributed with parameter λ2 = 2. A battery has been picked randomly and is still working after two months. Given this information, what is the probability that the first battery was picked?
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